高考中的数学文化

第一章 数学文化总论 ··················································································· 1 第一节 什么是数学文化 ········································································ 1 第二节 数学文化的四个层面 ································································· 3 一、知识系统 ······················································································· 4 二、工具系统 ······················································································· 4 三、价值系统 ······················································································· 5 四、史实系统 ······················································································· 7 第三节 数学文化的人本特性 ································································· 7 一、精神特性 ······················································································· 8 二、物质特性 ······················································································· 8 三、行为特性 ······················································································· 9 四、审美特性 ······················································································· 9 第二章 数学历史 ························································································ 11 第一节 数学名著 ················································································ 11 一、《九章算术》 ················································································ 12 二、《数书九章》 ················································································ 19 三、《算数书》 ··················································································· 24 第二节 数学故事 ················································································ 27 一、毕达哥拉斯的故事 ········································································· 27 二、高斯的故事 ·················································································· 36 三、哥德巴赫的故事 ············································································ 41 第三节 数学名题 ················································································ 44 一、米勒问题 ····················································································· 45 二、斐波那契数列 ··············································································· 57 三、阿基米德穷竭法 ············································································ 66 四、柯西不等式 ·················································································· 73 五、角谷猜想 ····················································································· 80 六、阿波罗尼奥斯圆 ············································································ 85 七、回文数 ························································································ 93 八、勾股数 ························································································ 98 九、平均数 ······················································································· 101 十、皮克定理 ···················································································· 108 十一、数字黑洞 ················································································· 114 十二、伯努利不等式 ··········································································· 119 十三、正整数方幂和 ··········································································· 124 十四、切比雪夫多项式 ········································································ 130 十五、马尔科夫定理 ··········································································· 135 十六、四色问题 ················································································· 143 十七、莱布尼茨三角形 ········································································ 146 十八、黄金分割比 ·············································································· 151 第三章 数学精神 ······················································································· 155 第一节 理性求真 ··············································································· 155 第二节 创新意识 ··············································································· 167 第四章 数学应用 ······················································································· 177 第一节 营销决策类 ············································································ 178 第二节 金融经济类 ············································································ 183 第三节 环境保护类 ············································································ 188 第四节 建设工程类 ············································································ 195 第五节 交通运输类 ············································································ 204 第六节 概率统计类 ············································································ 209 第七节 日常民生类 ············································································ 218 第五章 数学之美 ······················································································· 227 第一节 和谐美 ··················································································· 227 一、结构形式的和谐统一 ····································································· 228 二、项、项数、次数的和谐统一 ···························································· 235 三、转换的和谐统一 ··········································································· 239 第二节 简洁美 ··················································································· 242 第三节 对称美 ··················································································· 248 第四节 奇异美 ··················································································· 253 一、解法多样的奇异美 ········································································ 254 二、解法之巧的奇异美 ········································································ 259 第六章 数学语言 ······················································································· 264 第七章 交汇拓展 ······················································································· 272 第八章 数学游戏 ······················································································· 276 附录一 本书习题参考答案 ········································································· 285 附录二 高考数学文化最新动态 ································································· 325 参考文献 ···································································································· 344